Whakaoti i te {ccc}{6}&{-2}&{9}{-2}&{3}&{-1}{9}&{-1}&{3}

Aromātai

Tauwehe

Pātaitai

Ngā Raru Ōrite mai i te Rapu Tukutuku

https://socratic.org/questions/how-do-you-find-the-value-of-the-determinant-6-3-1-0-3-3-9-0-0

https://socratic.org/questions/how-do-you-find-the-determinant-of-2-1-3-3-0-2-1-3-0

https://socratic.org/questions/how-do-you-find-the-determinant-of-4-6-7-3-2-4-1-1-1

https://socratic.org/questions/how-do-you-find-the-determinant-of-0-1-4-3-2-3-8-3-4

https://socratic.org/questions/how-do-you-find-the-value-of-the-determinant-4-1-0-5-15-1-2-10-7

https://socratic.org/questions/how-do-you-find-the-determinant-of-8-9-3-3-5-7-1-2-4

Tohaina

Kua tāruatia ki te papatopenga

det(\left(\begin{matrix}6&-2&9\\-2&3&-1\\9&-1&3\end{matrix}\right))

Kimihia te tau whakatau o te poukapa mā te whakamahi i te tikanga hauroki.

\left(\begin{matrix}6&-2&9&6&-2\\-2&3&-1&-2&3\\9&-1&3&9&-1\end{matrix}\right)

Whakaroatia te poukapa taketake mā te tāruarua i ngā tīwae tuatahi e rua hei tīwae tuawhā me te tuarima.

6\times 3\times 3-2\left(-1\right)\times 9+9\left(-2\right)\left(-1\right)=90

Tīmata atu i te tāurunga mauī o runga, whakareatia whakararo i ngā hauroki, ka tāpiri i ngā hua ka puta.

9\times 3\times 9-\left(-6\right)+3\left(-2\right)\left(-2\right)=261

Tīmata atu i te tāurunga mauī o raro, whakareatia whakarunga i ngā hauroki, ka tāpiri i ngā hua ka puta.

90-261

Tangohia te tapeke o ngā hauroki whakarunga mai i te tapeke o ngā hua hauroki whakararo.

-171

Tango 261 mai i 90.

det(\left(\begin{matrix}6&-2&9\\-2&3&-1\\9&-1&3\end{matrix}\right))

Kimihia te tau whakatau o te poukapa mā te whakamahi i te tikanga whakaroha ā-tauriki (te tikanga whakaroha ā-tauwehe tahi rānei).

6det(\left(\begin{matrix}3&-1\\-1&3\end{matrix}\right))-\left(-2det(\left(\begin{matrix}-2&-1\\9&3\end{matrix}\right))\right)+9det(\left(\begin{matrix}-2&3\\9&-1\end{matrix}\right))

Hei whakaroha mā ngā tauriki, me whakarea ia huānga o te haupae tuatahi ki tana tauriki, arā, ko te tau whakatau o te poukapa 2\times 2 i hangā mā te muku i te haupae me te tīwae i roto anō taua huānga, kātahi ka whakarea ki te tohu tūnga o taua huānga.

6\left(3\times 3-\left(-\left(-1\right)\right)\right)-\left(-2\left(-2\times 3-9\left(-1\right)\right)\right)+9\left(-2\left(-1\right)-9\times 3\right)

Mō te poukapa 2\times 2 \left(\begin{matrix}a&b\\c&d\end{matrix}\right), ko te tau whakatau ko ad-bc.

6\times 8-\left(-2\times 3\right)+9\left(-25\right)

Whakarūnātia.

-171

Tāpirihia ngā kīanga tau hei kimi i te otinga whakamutunga.